The Liverpool team of 87/88 is generally regarded as our greatest side ever. The peak of that team was the 5-0 win over Forest at Anfield when Forest were still one of the top sides in the country. Sir Tom Finney described that match as the greatest performance he had ever seen, and the Liverpool side as the best he had ever seen. They won the league, and lost to Wimbledon in the cup final, in possibly the biggest upset in FA cup final history. Deffo the best team not to win the double.
That was around the time I started watching football, and watching that team, and especially John Barnes, there was no way I could ever be a blue.
I don't know if they were the best side ever, as it's too hard to judge different eras, and there were a lot of great sides around before my time, but they're the best I've seen. The Milan team of the early nineties was close to getting my vote though.